Experimental Determination of Air/Water Partition Coefficients for 21 Per- and Polyfluoroalkyl Substances Reveals Variable Performance of Property Prediction Models

Per- and polyfluoroalkyl substances (PFAS) are a group of chemicals of high environmental concern. However, reliable data for the air/water partition coefficients (Kaw), which are required for fate, exposure, and risk analysis, are available for only a few PFAS. In this study, Kaw values at 25 °C were determined for 21 neutral PFAS by using the hexadecane/air/water thermodynamic cycle. Hexadecane/water partition coefficients (KHxd/w) were measured with batch partition, shared-headspace, and/or modified variable phase ratio headspace methods and were divided by hexadecane/air partition coefficients (KHxd/air) to obtain Kaw values over 7 orders of magnitude (10–4.9 to 102.3). Comparison to predicted Kaw values by four models showed that the quantum chemically based COSMOtherm model stood out for accuracy with a root-mean-squared error (RMSE) of 0.42 log units, as compared to HenryWin, OPERA, and the linear solvation energy relationship with predicted descriptors (RMSE, 1.28–2.23). The results indicate the advantage of a theoretical model over empirical models for a data-poor class like PFAS and the importance of experimentally filling data gaps in the chemical domain of environmental interest. Kaw values for 222 neutral (or neutral species of) PFAS were predicted using COSMOtherm as current best estimates for practical and regulatory use.

Table S1.List of PFAS used in this study with their providers and purity.
Table S2.SMILES strings for PFAS used in this study.
Table S3.Experimental parameters for batch partition and shared-headspace methods.Table S4.Statistics of the regression lines in Figure 1.
Table S5.Log Kaw values obtained via eq 1 and predicted by various models.
Table S6.Indicators of applicability domains (AD) provided by OPERA and LSER-IFSQSAR.
Table S7.Log Kaw values of neutral (or neutral species of) PFAS predicted by COSMOtherm.

Batch partition method
Pure PFAS were dissolved in hexadecane either directly or using acetone as carrier solvent.Up to three PFAS were mixed in hexadecane and investigated simultaneously.The PFAS concentration in hexadecane was 0.1-2000 mg/L, depending on the expected KHxd/w and the sensitivity of the quantification method.The acetone content in hexadecane was up to 0.3% (v/v).This acetone should have largely partitioned into water during the partition experiment, where the final concentration in water was estimated to be < 0.3% (v/v).We assumed that this concentration of acetone in water does not have a significant influence on partition coefficients of PFAS.
Batch partition experiments were performed in 10-mL glass vials, which received water and the hexadecane solution of PFAS.The volume of water (Vw) was 1-5 mL, and that of hexadecane was 10 mL -Vw.Five replicate vials were prepared.The vials were crimp-sealed with PTFE-lined septa and were gently shaken for 24 h in an incubation chamber (60 rpm, 25 °C) while kept upright without breaking the hexadecane/water interface.The vials were then collected, flipped upside down slowly so that the water phase came into contact with the septum and kept standing for at least 30 min.An aliquot of the water phase was withdrawn through the septum using a Hamilton syringe.The vials were flipped back, the septum was removed, and the hexadecane phase was taken with a pipette.
The water phase was analyzed directly by liquid chromatography/mass spectrometry (LC/MS) (for PFBSA, PFHxSA, MeFBSA, MeFHxSA, MeFBSE), diluted with acetonitrile and analyzed with LC/MS (for PFOSA EtFHxSA, EtFHxSE), or liquid-liquid-extracted with n-hexane and analyzed by gas chromatography/mass spectrometry (GC/MS) (for all others).The hexadecane phase was backextracted with water (for PFBSA, PFHxSA) or with 0.1 mM NaOH water (for PFOSA) and measured by LC/MS, or it was diluted with n-hexane by a factor of 100-500 and analyzed by GC/MS (for all others).
KHxd/w was calculated using the measured water phase concentration under the mass conservation assumption.This assumption was confirmed by the hexadecane analysis, which demonstrated 93-112% of the expected concentrations in hexadecane.Note that back-extraction for PFBSA, PFHxSA, and PFOSA was not complete and was corrected for the extraction efficiency determined in a separate batch test.The 95% confidence interval (CI) of the mean (x) was calculated with the formula, x ± 2.78 SD/√5, where SD is the standard deviation, based on the t-distribution and n = 5.The PFAS concentrations prepared in hexadecane, water and hexadecane volumes, and recovery from the hexadecane phase for each PFAS are given in Table S2.Note that, as stated in the main text, PFBSA, PFHxSA, PFOSA, MeFBSA, MeFHxSA, and EtFHxSA were performed using 1 mM HCl aqueous solution instead of pure water.

Shared-headspace method
A shared headspace method was used to measure KHxd/w for nine PFAS.In this method, hexadecane solution of PFAS was prepared as described above and 300 μL was placed in a 350-μL glass insert accommodated by a 1.5-mL GC vial.This small vial was kept open and put in a 10-mL headspace vial that contains 1 mL of water.The 10-mL vial was closed with a PTFE-lined septum and gently shaken at 25 °C for 24 h.During this equilibration time, the PFAS dissolved in hexadecane was partially transferred to water via the headspace until three-phase partition equilibrium was reached between hexadecane, air, and water.The 10 mL vial was then opened, and water was sampled with a glass pipette and immediately extracted with n-hexane for GC/MS analysis.The hexadecane phase was also sampled, diluted with n-hexane, and measured with GC/MS, which confirmed 85-100% mass conservation (Table S2).KHxd/w was obtained from the measured concentration in water, as done in the batch partition method.

Modified VPR-HS method
KHxd/w was also measured with a modified version of VPR-HS method; 20 mL headspace vials were filled with water and hexadecane with a total liquid volume of 20 mL, leaving a headspace volume of 2.2 mL.All vials received 5 μL of acetonic stock solution (5 or 10 g/L).The vials were shaken standing for 22 h at a room temperature and placed in a GC-sample tray (Tray Cooler 2, Gerstel) controlled at 25.0 °C for 2 h.The headspace was sampled with a syringe using an autosampler and injected into the GC/MS.GC/MS conditions for the headspace measurement have been described previously.S2, the repeatability was high even without IS, with a relative standard deviation of 11% in the worst case.A single point calibration was performed as the response linearity was generally high.The concentration of the external standard was greater than the sample concentration but less than 10 times greater.

SI-3 Direct measurement of Kaw using VPR-HS method
Pure liquid or solid of PFAS (ca 1 μL or 1 mg) was directly dissolved in 20 or 200 mL of water.The solution was shaken for 24 h in a sealed container and distributed into 15 of 20-mL headspace vials.
The volumes of water in the vials were varied in the range of 0.1 to 3 mL or 1 to 16 mL.The headspace vials were closed with PTFE-lined septa, weighed, and equilibrated at 25°C for at least 2 h.The internal volume of the vials was 22.16 ± 0.09 mL, as measured before. 1 The vials were put on a sample tray (Tray Cooler 2, Gerstel) where the temperature was controlled at 25 °C.The headspace was then sampled and measured by using the GC/MS system (7890A GC/5975C MS, Agilent Technologies; MPS2 autosampler, Gerstel).The analytical conditions of GC/MS were the same as described in ref 1.
Under the mass conservation assumption, the measured GC peak area (PA) can be expressed as eq where r is the response factor between PA and the concentration of the analyte in the headspace, Cw is the initial concentration of the analyte in water, and VHS/Vw is the headspace-to-water volume ratio.
The equation was fitted to the data by adjusting rCw and Kaw using GraphPad Prism 9.5 with weighting factors (1/y 2 ).For more details about data evaluation, see ref 1.

SI-4 Possible presence of hexadecane in water samples of the batch partitioning experiment
The batch partition method-measured log KHxd/w values for five compounds (i.e., 4:2 FTI, 6:1 FTI, 6:1 FTI-7H, 6:2 FTAC, 4:2 FTMAC) were all ~4, which may be explained by possible hexadecane microdroplets in water.If hexadecane is present in the water sample, the apparent aqueous phase concentration of the chemical (Cw,app) can be expressed as the sum of the contributions from water and hexadecane to the total concentration; thus, where Cw is the true aqueous phase concentration of the chemical and φw and φHxd are the volume fractions of water and hexadecane, respectively, in the water sample.The corresponding apparent KHxd/w measured in the batch partition method (KHxd/w,app) is, where CHxd is the chemical concentration in hexadecane.Since CHxd/Cw = KHxd/w and φw ~ 1, eq S3 can be rewritten as, By rearranging eq S4, we obtain, By inserting the KHxd/w,app value measured by the batch partition method and the KHxd/w value measured by the shared-headspace method in eq S5, we can obtain the value of φHxd.The values of φHxd obtained this way for 4:2 FTI, 6:1 FTI, 6:1 FTI-7H, 6:2 FTAC, and 4:2 FTMAC were 0.000043 to 0.000073, with the mean of 0.000060 (or 0.0060%).

SI-5 Evaluation of new Kaw data in the literature
In the course of this work, a new paper appeared that reported Kaw values for 15 PFAS measured by the VPR-HS method. 5These data, however, are inconsistent with the available knowledge for Kaw of PFAS, as explained below.

Contents SI- 1
Figure SI-5-1.Dependence of log Kaw on the number of CF2.

Figure S1 .
Figure S1.Schematic illustrations of experimental methods for determination of partition coefficients.

Figure S2 .
Figure S2.The results of log KHxd/w determination by the modified VPR-HS method.

Figure S3 .
Figure S3.The results of log Kaw determination by the standard VPR-HS method.

Figure S4 .
Figure S4.Predicted vs experimental log Kaw (enlarged version of Figure 2 in the main manuscript).
Figure S6 compares the data from ref 5 to predictions by COSMOtherm computed in this study.For comparison, experimental data from this study are also included in the plot.Many data from ref 5 strongly deviate from COSMOtherm predictions.Errors of many orders of magnitude in COSMOtherm predictions are unlikely for such simply structured PFAS, considering the good agreement of predictions and experimental data from the current study.It should also be noted that the data from ref 5 include 4 acids (3 FTSs and 8:2 FTCA), which dissociate and become ionic in pure water.Thus, the apparent Kaw values measured around neutral pH (which are displayed in Figure S6) should be substantially lower than the actual Kaw values for the neutral species.However, the apparent Kaw data from ref 5 are higher than the COSMOtherm values for the neutral species by up to 5.5 log units.Additionally, it is inconsistent that the log Kaw values for 6:2 FTI (−0.52) and 8:2 FTAC (−0.50) from ref 5 are lower than the experimental values for 4:2 FTI (1.60) and 6:2 FTAC (1.27),

Figure S2 .
Figure S2.The results of log KHxd/w determination by the modified VPR-HS method.The mean and its 95% CIs of log KHxd/w obtained by model fitting are shown within the figure.The solid line indicates the model fit, and the dotted lines the 95% CIs of model fit.

Figure S3 .
Figure S3.The results of log Kaw determination by the standard VPR-HS method.The mean and its 95% CIs of log Kaw obtained by model fitting are shown within the figure.The solid line indicates the model fit, and the dotted lines the 95% CIs of model fit.

1 SI-2 Conditions for LC/MS and GC/MS analysis LC/MS analysis
The hexadecane peak usually appeared after all target PFAS had been eluted.The MS conditions were as following: ion source temperature, 230 °C; quadrupole temperature, 150 °C; gain factor, 1.The selected ion monitoring (SIM) mode was used for quantification.Two or three major ions were monitored for each PFAS.For quantification of the n-hexane extracts of water samples, internal standards (IS) were added to the extracts.The PFAS was quantified relative to the IS peak area.The compounds used as IS were: 4:2 FTOH for 5:2s and 6:2 FTOHs; 5:2s FTOH for 3:3, 4:2, and 4:4 FTOHs; 6:2 FTOH for 7:1 and 8:2 FTOHs; 6:2 FTI for 4:2 FTI, 6:1 FTI, 6:1 FTI-7H, 6:2 FTAC, and 4:2 FTMAC.For hexadecane samples diluted by n-hexane, no IS was added, and peak areas of PFAS were directly used for quantification.As shown in Table measured the dimensionless Henry's law constant kH, which is identical to Kaw Kaw from this study and refs 5 and 6 are plotted against the number of CF2 units to check the data consistency.As discussed in the manuscript, the data from this study showed consistent slopes (0.43 ± 0.02) across different classes of PFAS.The data from Goss et al.
6also showed a comparable slope (0.53 ± 0.03).The data from ref 5, however, indicated a slope of 0.20 ± 0.06 (FTOHs) and 0.08 ± 0.03 (FTSs), significantly smaller than those of the former two studies.As discussed by Goss et al.,6such a gentle slope is unlikely considering the hydrophobic nature of the perfluoroalkyl structure.

Table S1 .
List of PFAS used in this study with their providers and purity.

Table S3 .
Experimental parameters for batch partition and shared-headspace methods.

Table S4 .
Statistics of the regression lines in Figure1.

Table S5 .
Log Kaw values obtained via eq 1 and predicted by various models.

Table S6 .
Indicators of applicability domains (AD) provided by OPERA and LSER-IFSQSAR.

Table S7 .
Log Kaw values of neutral (or neutral species of) PFAS predicted by COSMOtherm.